{
  "id": "1911.03009",
  "version": "v1",
  "published": "2019-11-08T02:58:46.000Z",
  "updated": "2019-11-08T02:58:46.000Z",
  "title": "Set-theoretic Yang-Baxter (co)homology theory of involutive non-degenerate solutions",
  "authors": [
    "Józef H. Przytycki",
    "Petr Vojtěchovský",
    "Seung Yeop Yang"
  ],
  "comment": "11 pages, 6 figures",
  "categories": [
    "math.GT",
    "math.AT"
  ],
  "abstract": "W. Rump showed that there exists a one-to-one correspondence between involutive right non-degenerate solutions of the Yang-Baxter equation and Rump right quasigroups. J. S. Carter, M. Elhamdadi, and M. Saito, meanwhile, introduced a homology theory of set-theoretic solutions of the Yang-Baxter equation in order to define cocycle invariants of classical knots. In this paper, we introduce the normalized homology theory of an involutive right non-degenerate solution of the Yang-Baxter equation and prove that the set-theoretic Yang-Baxter homology of certain solutions can be split into the normalized and degenerated parts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-08T02:58:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T25",
      "20N05",
      "57M27"
    ],
    "keywords": [
      "homology theory",
      "involutive non-degenerate solutions",
      "involutive right non-degenerate solution",
      "yang-baxter equation",
      "rump right quasigroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}